These investigations also lead to deeper insights into the geometric structure and local isometry types of the manifolds under study.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:In this study, we consider various geometric conditions associated with the vanishing of a generalized curvature tensor, namely the $\mathcal{T}$-tensor, on $N(\kappa)$-contact metric manifolds.
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Temel Bulgular & Veri:We define and analyze several types of $\mathcal{T}$-flatness conditions, including $\mathcal{T}$-flat, $\xi$-$\mathcal{T}$-flat, quasi-$\mathcal{T}$-flat, and $\varphi$-$\mathcal{T}$-flat structures.
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Sonuç & Katkı:These investigations also lead to deeper insights into the geometric structure and local isometry types of the manifolds under study.
In this study, we consider various geometric conditions associated with the vanishing of a generalized curvature tensor, namely the $\mathcal{T}$-tensor, on $N(\kappa)$-contact metric manifolds. We define and analyze several types of $\mathcal{T}$-flatness conditions, including $\mathcal{T}$-flat, $\xi$-$\mathcal{T}$-flat, quasi-$\mathcal{T}$-flat, and $\varphi$-$\mathcal{T}$-flat structures. By applying these flatness conditions, we obtain algebraic constraints on the curvature parameters, particularly involving the Ricci tensor. The resulting characterizations allow for the classification of $N(\kappa)$-contact metric manifolds as either Einstein or $\eta$-Einstein, depending on the specific values of the structure constants. These investigations also lead to deeper insights into the geometric structure and local isometry types of the manifolds under study.
Ünal, İ., Altın, M., Pandey, S. (2025). A Classification of $ N(\kappa)$-contact Metric Manifolds with $ \mathcal{T} $-curvature Tensor. Turkish Journal of Mathematics and Computer Science, Volume: 17 Issue: 2. https://doi.org/10.47000/tjmcs.1632911
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